Conventionally, there have been proposed an M-sequence, Kasami-codes, a Gold sequence or the like which are generated by a linear feedback shift register (LFSR) as spreading codes which realize spectrum spread communication and code division multiplex communication. Those spreading code sequences have the following two features.
First, there is a single peak in the correlation (autocorrelation) between same codes and the correlation (cross-correlation) between different codes is 0. This is extremely analogous to the property of white noise.
Secondly, in case where two different spreading codes included in a set of codes are selected and in case where a code set is constructed in such a way that if either one is selected, the cross-correlation comes closer to 0, the number of codes included in the code set is merely 0(N) with respect to a code length N. Therefore, there are few kinds of codes.
Meanwhile, there have also been known TDMA (Time Division Multiple Access) and FDMA (Frequency Division Multiple Access). Unlike those, the asynchronous CDMA communication system has a feature that decoding is possible by using the correlation characteristics of codes to be used without positively taking synchronism of signals. Therefore, it is excellent in security, confidentiality, anti-interference, disturbance and so forth.
At present, the asynchronous CDMA communication system is undergoing the practical use stage and its use has been decided as the ITU (International Telecommunication Union) standard for wireless communication of the next generation called IMT-2000 (International Mobile Telecommunication 2000).
It is known from the recent studies that in the asynchronous CDMA communication system, the variance σ of intersymbol interference noise determines the performance of the system. It is disclosed in, for example, the following document that in case where pseudo white noise, such as a Gold-code or Kasami-code, is used as a spreading code, the variance σ is asymptoticallyσ=(K−1)/3Nwhere K is the number of simultaneously connected users and N is the code length.
M. B. Pursley, “Performance Evaluation for Phased-Coded Spread-Spectrum Multiple-Access Communication-Part I: System Analysis” (IEEE Trans. Communications, vol. 25 (1977) pp. 795-799.)
Here, “asymptotically” means a case where the user number K and the code length N taken are large.
Conventionally, the theoretical limit of the performance of the asynchronous CDMA communication system was considered to be this σ=(K−1)/3N. However, it was also known that satisfying such an asymptotical relationship was originated from spreading codes being pseudo white noise.
In case where spreading codes are not pseudo white noise, i.e., in case where there is some correlation between different codes, however, the theoretical limit of the performance may be improved.
Recently has been discovered the existence of spreading codes which have an autocorrelation function such that the variance a of intersymbol interference noise is reduced as compared with σ case where spreading codes are pseudo white noise. That is, in case where an autocorrelation function C(s) decreases exponentially as follows with respect to a code shift amount sC(s)≅Const.×(−r)−s(0<r<1),
the variance σ of intersymbol interference noise becomes smaller than that in the case of pseudo white noise.
In case where a real impulse constant r satisfiesr=2−31/2,particularly, it takes the form of the following optimal correlation functionσoptimal=31/2(K−1)/(6N).
This means that the number of simultaneously connected users, K, at the same bit error rate is increased by 15% from the theoretical limit of the user number of the asynchronous CDMA communication system when pseudo white noise is used as a spreading code. This point is disclosed in the following document.
G. Mazzini, R. Rovatti, and G. Setti “Interference Minimization by Auto-Correlation Shaping in Asynchronous DS-CDMA Systems: Chaos-Based Spreading is Nearly Optimal” (Electron. Lett. (1999) vol. 35, pp. 1054-1055)
The document illustrates that a correlation function C(s) which satisfies the above condition can be approximately typified by constructing chaos-based spreading codes using a piecewise linear map whose partial slope is extremely large.
To actually generate such a spreading sequence using a DSP (Digital Signal Processor) or the like and use in a portable phone or the like, however, high speed and low consumed power are needed, so that the following problems would arise.
First, there was a problem that as spreading codes were composed of a piecewise linear map whose partial slope is extremely large, executing computation by a DSP or computer or the like increased digit drop so that accurate results could not be obtained. This has brought about a matter that it is difficult to generate spreading codes in physical circuits or devices.
Secondly, there was a problem that a parameter which determines the manner of attenuation of a correlation function could not be adjusted freely with respect to an arbitrary r (−1<r<1).
Thirdly, the aforementioned document shows that there are few types of piecewise linear maps having correlation functions close to the optimal correlation function. To realize a CDMA communication system, however, it is better to provide as many kinds of codes as possible. Therefore, the use of the scheme disclosed in the aforementioned document made it difficult to actually construct a CDMA communication system.
Fourthly, with spreading codes generated by using a linear shift register, the types of codes with a good correlation characteristic with respect to the code length N are merely 0(N). This is very small whereas the proper types of codes should be a number 0(2N) proportional to the power of 2. It is therefore difficult to cope with an increase in the number of users.
Fifthly, as the key space is narrow, there is less work needed for decoding. This raises a problem that the communication security becomes weaker.
The technique disclosed in the aforementioned document has not improvements made on those problems.
Therefore, there is a strong demand for a technique of generating spreading codes composed of a pseudorandom sequence (also called PN (Pseudo Noise) sequence) suitable for an asynchronous CDMA communication system while overcoming those problems.
There has been proposed a wireless communication technique by a system, such as the IMT-2000 W-CDMA system, 1CDMA 2000 system, Wireless LAN IEEE 802.11b or the like. As such wireless communication uses the same frequency band for plural communication connections, CDMA (Code Division Multiple Access) is utilized.
In the CDMA, plural communication connections can be put in the same frequency band or a desired communication connection can be separated from the same frequency band by spread-modulating communication information using different spreading codes.
Meanwhile, in those wireless communications, it is typical to transform information to be transferred into a complex number sequence, then perform a process.
Therefore, there is a demand for a simple technique for performing spread modulation using spreading codes which has an excellent separability in such a wireless communication technology.
Further, there has been proposed a spectrum spreading technique which uses, as spreading codes, an orthogonal code sequence (including an M-sequence, Gold-codes, an orthogonal code sequence acquired from a Walsh function, an orthogonal code sequence acquired from a Chebyshev's polynomial, a Baker sequence and a Manchester-coded orthogonal sequence; the same applied hereinafter).
As the same frequency band is used in plural communication connections in a wireless communication technique using systems, for example, the IMT-2000 W-CDMA system, 1CDMA 2000 system and Wireless LAN IEEE 802.11b, CDMA (Code Division Multiple Access) is used.
In the CDMA, a complex number in which elements of an orthogonal code sequence are placed in a real portion and an imaginary portion is a spreading code and plural communication connections can be put in the same frequency band or a desired communication connection can be separated from the same frequency band by spread-modulating communication information using different spreading codes.
In such a wireless communication technique, communication often takes place between a base station and a mobile terminal, but generally, first, a mobile terminal sends a signal to a base station (Up Link communication) and the base station receives it and takes synchronization, then communication is performed between both.
At the time of starting communication between both, therefore, synchronization is taken by getting a correlation on the then receiver side (which is generally the base station but may be the mobile terminal in some case).
Meanwhile, communication after synchronization (Down Link communication) has only to perform synchronization detection because synchronization has been taken beforehand.
In such a wireless communication technique, there is always a demand for a communication technique which has an excellent separability and has a low BER (Bit Error Rate) even if users are increased.
Further, there are large demands for an apparatus and devices that can perform a filter process which is used in a general-purpose fashion at the time of solving those problems. It is deemed that such a filter process has a wide range of application of to other fields.
The present invention aims at providing a filter apparatus, a receiving apparatus, a transmitting apparatus, a pseudorandom sequence output apparatus, a filter method, a receiving method, a transmitting method and a pseudorandom sequence output method, which are suitable in such various usages, and a program which realizes them on a computer.